A BMI of less than 19 is considered underweight. A BMI between 19 and 25 inclusive is considered in the healthy weight range. A BMI above 25 but below 30 is considered overweight, while a BMI of 30 and above is considered obese.
Modify the program so that it prints out an appropriate health advisory.

if BMI < 19:
print " You are currently underweight"
elif BMI >= 19:
print " You are in a healthy weight range"

You will never get past these two statements as they cover every possibility. Note also, that the second "elif BMI >= 19:" is not necessary as after the first if statement that is the only remaining possibility. Do this with functions instead as that will be easier to understand, then you can convert back to if statements if you want to.

def less_than_19():
print " You are currently underweight"
def greater_than_19(BMI):
if BMI <= 25:
print "You are still in a healthy weight range"
return
elif BMI < 30:
print "You are in the overweight range. Please see your doctor"
return
else: ## has to be >= 30
print " You are obese. Please make some changes and see your doctor"
if BMI < 19:
less_than_19()
else:
greater_than_19(BMI)

Generally speaking, we don't provide complete answers for homework problems, but hints to help the OP figure it out for themselves. Homework is meant to be a learning tool. And usually it is coded
elif 19 < BMI <= 25:
but is at the individual's preference of course.

Using the OP's original code, it would be something like the following, since an and statement is the same as nested if statements (both Gribouillis and I were hinting at separate blocks for each level, i.e. an additional indent).

if BMI < 19:
print " You are currently underweight"
else:
## can only be >= 19 ------------------------------------------
if BMI <= 25: ## else is the >= 19
print "You are still in a healthy weight range"
else:
## can only be > 25 ---------------------------------------
if BMI < 30:
print "You are in the overweight weight range. Please see your doctor"
else:
## can only be >= 30 ----------------------------------
print " You are obese. Please make some changes and see your doctor